This note investigates the regularity of zero-extensions of $L^p$ functions from bounded domains. Simple examples show the possibility of a loss in smoothness and our goal is to quantify this loss more generally. For the unit cube $\mathcal{Q}=[0,1...
Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ denote the connected component of the diffeomorphism group of $M$ containing the identity. The natural action of $G$ on $M$ induces the trace homomorphism on homology. We show...
Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but non-smooth. We sho...
In this short note, we present a trick to ensure that the Jacobian of a given smooth curve has strictly positive Mordell-Weil rank. More explicitly, we prove that a smooth curve with no rational non-trivial 2-torsion and no rational theta characteris...
Randomized smoothing is a leading approach for constructing classifiers that are certifiably robust against adversarial examples. Existing work on randomized smoothing has focused on classifiers with continuous inputs, such as images, where $\ell_p$-...
We study a $K$-armed non-stationary bandit model where rewards change smoothly, as captured by Hölder class assumptions on rewards as functions of time. Such smooth changes are parametrized by a Hölder exponent $β$ and coefficient $λ$. While vari...
Delicious and nutritious smoothies that combine the best ingredients to nourish your body! We did the work for you, so you don't have to! Pop 8 Evive cubes, add 250 ml of water, and blend (or shake!). …
The objective of this project is to implement and present the results that were obtained by Z. Farbman, R. Fattal, D. Lischinski, and R. Szeliski in "Edge-preserving decompositions for multi-scale tone and detail manipulation, ACM Transactions on Graphics (TOG), 2008" (⭐ 1)
About: AEON was launched on 6.6.2014 at 6:00 PM UTC, with no premine or instamine. AEON is for people who want to pay and live freely, who want to be part of the cryptocurrency revolution and want to try something new. It is based on the CryptoNote protocol and uses the CryptoNig…
Over a field k of characteristic 3, we prove that there are no smooth quartic surfaces S in IP^3 with more than 112 lines. Moreover, the surface with 112 lines is projectively equivalent over k-bar to the Fermat quartic. As a key ingredient, we deriv...
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of executing...
Apr 18, 2019 · You can say "more smooth", or "smoother". Both are fine and mean exactly the same thing. But beware of trying to combine them, and saying "more smoother"! Many will say that a …
This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard techniques in the study of oscillatory integrals with the simpler toy mo...
Apr 18, 2019 · You can say "more smooth", or "smoother". Both are fine and mean exactly the same thing. But beware of trying to combine them, and saying "more smoother"! Many will say that a …
We present a novel method for convex unconstrained optimization that, without any modifications, ensures: (i) accelerated convergence rate for smooth objectives, (ii) standard convergence rate in the general (non-smooth) setting, and (iii) standard c...
Hard or Smooth is the second album released by Wreckx-n-Effect. It was released on November 24, 1992, by MCA Records, and featured production from Teddy
We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our me...
Trend filtering---first introduced into the astronomical literature in Paper I of this series---is a state-of-the-art statistical tool for denoising one-dimensional signals that possess varying degrees of smoothness. In this work, we demonstrate the...
Jul 23, 2025 · Is there a smooth function approximating the minimum of a constant and a variable? Ask Question Asked 7 months ago Modified 7 months ago
We compute the rate of convergence of forward, backward and central finite difference $θ$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and less smooth initi...